Calculating Average (x) and Sum (y) for Evaluation

First, we need to find the average, denoted by x, of the given five numbers: $2, 3, 5, 7, 13$.

Calculating Average x

The average is calculated by dividing the sum of the numbers by the count of the numbers.

• Sum of numbers = $2 + 3 + 5 + 7 + 13 = 30$
• Count of numbers = 5
• Average ($x$) = $\\frac{\\text{Sum}}{\\text{Count}} = \\frac{30}{5} = 6$

So, $x = 6$.

Calculating Sum y

Next, we identify the odd numbers between $10$ and $20$. These are $11, 13, 15, 17, 19$. We need to find their sum, denoted by y.

• Odd numbers = $11, 13, 15, 17, 19$
• Sum ($y$) = $11 + 13 + 15 + 17 + 19 = 75$

So, $y = 75$.

Evaluating Final Expression y - 2x

Finally, we calculate the value of the expression $y - 2x$ using the values we found for x and y.

• Substitute $x=6$ and $y=75$ into the expression $y - 2x$.
• $y - 2x = 75 - 2(6)$
• $y - 2x = 75 - 12$
• $y - 2x = 63$

The value of $y - 2x$ is $63$. This corresponds to Option D.